搁 is more colloquial than 放 (to put). It's very common in northern Chinese dialects. 搁 also implies leaving something for a while - 搁着 means 'to leave sitting there.' The internet phrase 搁这儿搁这儿呢 is a playful expression of disbelief.
扌 is the hand radical 手 in left-side form. It marks 搁 as a manual action, joining 放拿摆推 - characters where the hand does the verb. Setting something down with care is an action of placing.
阁 supplies the sound (gé drifted to gē) and a faint sense of putting away on a shelf - cabinets hold things stored aside. Combined with the hand radical, the character pictures the hand-action of setting items down on storage.
